İzi̇ Sifir Olan Jeneri̇k Matri̇sler Cebi̇ri̇ İçi̇n Nowicki Sanisi

Abstract

A locally nilpotent linear derivation δ of the commutative polynomial algebra K[Xd ]=K[x1,…,xd ] of rank d is called Weitzenböck. It is well known that the subalgebra K[Xd ]^δ of K[Xd ] consisting of polynomials which are sent to zero by δ is finitely generated. Let the Weitzenböck derivation δ act on K[Xd,Yd ] such that δ(yi )=xi, δ(xi )=0, i=1,…,d. The explicit form of generators of the algebra K[Xd,Yd ]^δ was conjectured by Nowicki in 1994. In this study, we consider the Nowicki conjecture in the algebra W generated by two traceless generic matrices with entries from commutative associative unitary polynomial algebra with six variables, and obtain the free generators of the algebra W^δ of constants in this algebra.